The Gaussian Model on the Inhomogeneous Fractal Lattices

The decimation real-space renormalization group and spin-rescaling methods are applied to the study of phase transition of the Gaussian model on fractal lattices. It is found that the critical point K^* equals b/2 ( b is the distribution constant of Gaussian model) on nonbranching Koch curves. For inhomogeneous fractal lattices, it is proposed that the b is replaced with b_qi (qi is the coordination number of the site i) and satisfies a certain relation b_qi/b_qj = q_i/q_j. Under this supposition we find that the critical point of the Gaussian model on a branching Koch curve can be expressed uniquely as K^* = b_qi/q_i.